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Solving the following equation without taking inverse.

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Parikshit Pareek
Parikshit Pareek 2017-6-21
编辑： Torsten 2022-3-25
How to solve the following equation for calculating the D:
D=|inv(B)|∗|g|
here, B is a non-singular square matrix and g is a column vector of the length equal to the no of elements in the row of B. Modules is applied element-wise.
The solution of this without taking the inverse.
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Walter Roberson
Walter Roberson 2022-3-25
@KHAN WALI
If it were not for the part of the then with singular matrices you would typically switch to using
What is the mathematical situation that leads you to want to have the part? And would using
D = abs(pinv(B)) * abs(g)
be acceptable for your situation?
Torsten
Torsten 2022-3-25
编辑：Torsten 2022-3-25
I also didn't read the title of the contribution and thought:
Why not simply
D = abs(inv(B))*abs(g)
?

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回答（1 个）

Chunru
Chunru 2022-3-25
Ran in:
In matlab, you can solve the linear system by mldivide or \
"doc mldivide" for detailed description.
B= randn(4, 4)
B = 4×4
-0.0294 0.1957 -1.5414 -0.1266 0.2383 0.9828 0.2350 -0.1879 -0.2651 -0.7456 1.1097 0.4562 -0.7198 -0.0695 -0.1106 0.3846
g = randn(4, 1)
g = 4×1
0.3455 -0.6763 -2.1197 -1.6276
f = B \ g
f = 4×1
-3.8263 -2.1101 0.5352 -11.6193
B * f
ans = 4×1
0.3455 -0.6763 -2.1197 -1.6276
  1 个评论
Walter Roberson
Walter Roberson 2022-3-25
Notice in the original question,
Modules is applied element-wise
That is, the we see is absolute value of each element of g, and the is absolute value of each element of the inverse of B.
It is easy enough in your code to use B\abs(g) so there is no concern about the part. But the MATLAB \ operator does not take absolute value of the inverse, and there is no option to force it to.
This feels like a constrained least squares. I wonder if https://www.mathworks.com/help/matlab/ref/lsqnonneg.html can be used?

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